[Solutions de Beltrami des équations d'équilibre de la mécanique des milieux continus]
M. Gurtin a montré que la représentation de Beltrami, , d'un champ régulier de contraintes à divergence nulle dans un ouvert à bord régulier est vérifiée si et seulement si S est auto-équilibré. Les conditions données par Gurtin sont étendues au cas d'un ouvert à bord Lipschitzien pour un champ . Par application de ce résultat on trouve une extension des conditions de compatibilité de Saint Venant aux domaines non nécessairement simplement connexes.
M. Gurtin has proved that the Beltrami representation, , of a smooth, divergence-free stress tensor in a smooth domain, is verified if and only if S is self-equilibrated. Here, Gurtin's conditions are extended to the case of a bounded domain with a Lipschitz-continuous boundary, for a tensor field . We apply this result to obtain an extension of the Saint Venant's equations of compatibility to non necessarily simply-connected domains.
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@article{CRMATH_2006__342_5_359_0,
author = {Geymonat, Giuseppe and Krasucki, Fran\c{c}oise},
title = {Beltrami's solutions of general equilibrium equations in continuum mechanics},
journal = {Comptes Rendus. Math\'ematique},
pages = {359--363},
publisher = {Elsevier},
volume = {342},
number = {5},
year = {2006},
doi = {10.1016/j.crma.2005.12.031},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2005.12.031/}
}
TY - JOUR AU - Geymonat, Giuseppe AU - Krasucki, Françoise TI - Beltrami's solutions of general equilibrium equations in continuum mechanics JO - Comptes Rendus. Mathématique PY - 2006 SP - 359 EP - 363 VL - 342 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2005.12.031/ DO - 10.1016/j.crma.2005.12.031 LA - en ID - CRMATH_2006__342_5_359_0 ER -
%0 Journal Article %A Geymonat, Giuseppe %A Krasucki, Françoise %T Beltrami's solutions of general equilibrium equations in continuum mechanics %J Comptes Rendus. Mathématique %D 2006 %P 359-363 %V 342 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2005.12.031/ %R 10.1016/j.crma.2005.12.031 %G en %F CRMATH_2006__342_5_359_0
Geymonat, Giuseppe; Krasucki, Françoise. Beltrami's solutions of general equilibrium equations in continuum mechanics. Comptes Rendus. Mathématique, Tome 342 (2006) no. 5, pp. 359-363. doi : 10.1016/j.crma.2005.12.031. http://www.numdam.org/articles/10.1016/j.crma.2005.12.031/
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